Basic Math Examples

$100 = z \sqrt{900 - 60 z}$

Step 1

Simplify $z \sqrt{900 - 60 z}$ .

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Step 1.1

Factor $60$ out of $900 - 60 z$ .

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Step 1.1.1

Factor $60$ out of $900$ .

$100 = z \sqrt{60 (15) - 60 z}$

Step 1.1.2

Factor $60$ out of $- 60 z$ .

$100 = z \sqrt{60 (15) + 60 (- z)}$

Step 1.1.3

Factor $60$ out of $60 (15) + 60 (- z)$ .

$100 = z \sqrt{60 (15 - z)}$

Step 1.2

Rewrite $60 (15 - z)$ as $2^{2} \cdot (15 (15 - z))$ .

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Step 1.2.1

Factor $4$ out of $60$ .

$100 = z \sqrt{4 (15) (15 - z)}$

Step 1.2.2

Rewrite $4$ as $2^{2}$ .

$100 = z \sqrt{2^{2} \cdot 15 (15 - z)}$

Step 1.2.3

Add parentheses.

$100 = z \sqrt{2^{2} \cdot (15 (15 - z))}$

Step 1.3

Pull terms out from under the radical.

$100 = z (2 \sqrt{15 (15 - z)})$

Step 1.4

Rewrite using the commutative property of multiplication.

$100 = 2 z \sqrt{15 (15 - z)}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$z \approx 3.86963143, 14.16993298$

Step 3